\[ \int \frac {1}{\sqrt {2-x} \sqrt {3-x} \sqrt {1+x}} \, dx \]
Optimal antiderivative \[ \EllipticF \left (\frac {\sqrt {1+x}\, \sqrt {3}}{3}, \frac {\sqrt {3}}{2}\right ) \]
command
integrate(1/(2-x)^(1/2)/(3-x)^(1/2)/(1+x)^(1/2),x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ 2 \, {\rm weierstrassPInverse}\left (\frac {52}{3}, -\frac {280}{27}, x - \frac {4}{3}\right ) \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left (\frac {\sqrt {x + 1} \sqrt {-x + 3} \sqrt {-x + 2}}{x^{3} - 4 \, x^{2} + x + 6}, x\right ) \]